In general, as we can observe with the Covid crisis, ordinary people recognise well the differences between how we should deal with an emergency as opposed to routine situations. Better indeed than some of their leaders or 'informed' commentators. But there is a special problem with climate change.
People naturally think of emergencies as short-term disturbances in the routine of everyday living. Wars, earthquakes, or pandemics may fit that well enough. Climate change does not. It is not an emergency in the ordinary sense, it is a change in routine. Moreover, it has the potential to be more all-encompassing than other changes in routine like technology, changing social customs and the like. When Montesquieu attempted to explain social practice in relation to climate he was assumed to be conservative. Nowadays he would be predicting world revolutions.
This is why it is so hard to pull people in behind radical action to deal with climate change. It's not once for all radical action and then the challenge is over. It's radical action for the long term.
This is all the harder, because with the partial exception of the 94 year old David Attenborough, no one is trusted to give a lead. In the age of 'postmodernism' or 'end of deference' (distinct but related phenomena) even scientific observations like shrinkage of ice caps do not impact much, except for those living in marginal regions where everyday living is already harder. Otherwise, it's the partisan divides, with Greta Thunberg a heroine or an irritant depending which side you are on.